Formula and method for Square Feet of a Triangle
The area of any triangle is exactly half of the rectangle formed by its base and a perpendicular height: A = ½ × base × height. This calculator multiplies your base and height, halves the result to get the true triangle area, and can also estimate a material purchase quantity (with a 10% waste allowance) and its cost.
How the calculation works
Enter the base of the triangle and its height — the height is the perpendicular (straight up-and-down) distance from the base to the opposite vertex, not the length of a slanted side. Multiply base × height to get the area of the enclosing rectangle, then divide by 2 to get the triangle's area: A = ½ × b × h. If base and height are both in feet, the area is in square feet (ft²); the calculator also multiplies the area by 1.10 to suggest a purchase quantity that allows for angled cuts, and multiplies that by an optional cost per square unit to estimate material cost.
Common mistakes
- Using a slanted side instead of the height: the height must be measured perpendicular to the base. Using the length of an angled side instead of the true perpendicular height overstates the area.
- Forgetting to halve: base × height gives the area of the surrounding rectangle, which is twice the triangle's actual area — always divide by 2.
- Mixing units: keep base and height in the same unit (both in feet, or both in meters) before calculating; mixing units produces an incorrect area.
Real-world applications
- Triangular rooms, decks, or lots use this formula to estimate square footage for flooring, sod, or paving (add about 10% extra material for angled cuts).
- Roofing and siding estimates use triangular gable-end area to calculate shingle or panel quantities.
- Landscaping and garden-bed design use triangle area to plan mulch, soil, or plant coverage for triangular plots.
- When only the three side lengths are known (no measured height), Heron's formula gives the same area without a perpendicular measurement.